First off,welcome to the forums!
Ok, i have had this game since the PSP came out, so im pretty good if i do say so myself

. Ok, what i do is i tap the brakes coming into a corner so that it will send me into the initial drift. From tehre its kind of a balancing act, just keep the car going at a reasonable angle through the turn. Personally, i drift every turn. Its faster, and it feels better since the vehicles can barely turn on their own without drifting. Also, i always try to keep at least one shot of nitrous for the last part of the last lap, because you never know when someone might pass you on that last straightaway, and you need just one shot of nitro to pass them and steal the win.
Those are my tips for now, so good luck and happy gaming.